Question

A fair dice is thrown eight times, then the probability that on the eighth throw, a third 6 is obtained, is

• A. ${}^7{C}_2\left(\frac{5^5}{6^6}\right)$
• B. ${}^7{C}_2\left(\frac{5^5}{6^7}\right)$
• C. ${}^7{C}_2{\left(\frac{5}{6}\right)}^7$
• D. ${}^7{C}_2\left(\frac{5^5}{6^8}\right)$

Answer 1

The correct option is D

${}^7{C}_2\left(\frac{5^5}{6^8}\right)$

Third 6 is obtained on the eighth throw, so 6 should appear two times in first 7 throws.

So, the required probability is

$={}^7{C}_2\times {\left(\frac{1}{6}\right)}^2\times {\left(\frac{5}{6}\right)}^5\times \frac{1}{6}$

$={}^7{C}_2\left(\frac{5^5}{6^8}\right)$